// -*- mode: rust; -*-
//
// This file is part of curve25519-dalek.
// Copyright (c) 2016-2019 Isis Lovecruft, Henry de Valence
// See LICENSE for licensing information.
//
// Authors:
// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
// - Henry de Valence <hdevalence@hdevalence.ca>

//! This module contains various constants (such as curve parameters
//! and useful field elements like `sqrt(-1)`), as well as
//! lookup tables of pre-computed points.

use backend::serial::curve_models::AffineNielsPoint;
use backend::serial::u32::field::FieldElement2625;
use backend::serial::u32::scalar::Scalar29;
use edwards::{EdwardsBasepointTable, EdwardsPoint};
use window::{LookupTable, NafLookupTable8};

/// The value of minus one, equal to `-&FieldElement::one()`
pub(crate) const MINUS_ONE: FieldElement2625 = FieldElement2625([
    67108844, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431
]);

/// Edwards `d` value, equal to `-121665/121666 mod p`.
pub(crate) const EDWARDS_D: FieldElement2625 = FieldElement2625([
    56195235, 13857412, 51736253, 6949390, 114729, 24766616, 60832955, 30306712, 48412415, 21499315,
]);

/// Edwards `2*d` value, equal to `2*(-121665/121666) mod p`.
pub(crate) const EDWARDS_D2: FieldElement2625 = FieldElement2625([
    45281625, 27714825, 36363642, 13898781, 229458, 15978800, 54557047, 27058993, 29715967, 9444199,
]);

/// One minus edwards `d` value squared, equal to `(1 - (-121665/121666) mod p) pow 2`
pub(crate) const ONE_MINUS_EDWARDS_D_SQUARED: FieldElement2625 =  FieldElement2625([
    6275446, 16937061, 44170319, 29780721, 11667076, 7397348, 39186143, 1766194, 42675006, 672202
]);

/// Edwards `d` value minus one squared, equal to `(((-121665/121666) mod p) - 1) pow 2`
pub(crate) const EDWARDS_D_MINUS_ONE_SQUARED: FieldElement2625 =  FieldElement2625([
    15551776, 22456977, 53683765, 23429360, 55212328, 10178283, 40474537, 4729243, 61826754, 23438029
]);

/// `= sqrt(a*d - 1)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub(crate) const SQRT_AD_MINUS_ONE: FieldElement2625 = FieldElement2625([
    24849947, 33400850, 43495378, 6347714, 46036536, 32887293, 41837720, 18186727, 66238516,
    14525638,
]);

/// `= 1/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub(crate) const INVSQRT_A_MINUS_D: FieldElement2625 = FieldElement2625([
    6111466, 4156064, 39310137, 12243467, 41204824, 120896, 20826367, 26493656, 6093567, 31568420,
]);

/// Precomputed value of one of the square roots of -1 (mod p)
pub(crate) const SQRT_M1: FieldElement2625 = FieldElement2625([
    34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654, 31548777, 326685, 11406482,
]);

/// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
pub(crate) const APLUS2_OVER_FOUR: FieldElement2625 =
    FieldElement2625([121666, 0, 0, 0, 0, 0, 0, 0, 0, 0]);

/// `L` is the order of base point, i.e. 2^252 +
/// 27742317777372353535851937790883648493
pub(crate) const L: Scalar29 = Scalar29([
    0x1cf5d3ed, 0x009318d2, 0x1de73596, 0x1df3bd45, 0x0000014d, 0x00000000, 0x00000000, 0x00000000,
    0x00100000,
]);

/// `L` * `LFACTOR` = -1 (mod 2^29)
pub(crate) const LFACTOR: u32 = 0x12547e1b;

/// `R` = R % L where R = 2^261
pub(crate) const R: Scalar29 = Scalar29([
    0x114df9ed, 0x1a617303, 0x0f7c098c, 0x16793167, 0x1ffd656e, 0x1fffffff, 0x1fffffff, 0x1fffffff,
    0x000fffff,
]);

/// `RR` = (R^2) % L where R = 2^261
pub(crate) const RR: Scalar29 = Scalar29([
    0x0b5f9d12, 0x1e141b17, 0x158d7f3d, 0x143f3757, 0x1972d781, 0x042feb7c, 0x1ceec73d, 0x1e184d1e,
    0x0005046d,
]);

/// The Ed25519 basepoint, as an `EdwardsPoint`.
///
/// This is called `_POINT` to distinguish it from
/// `ED25519_BASEPOINT_TABLE`, which should be used for scalar
/// multiplication (it's much faster).
pub const ED25519_BASEPOINT_POINT: EdwardsPoint = EdwardsPoint {
    X: FieldElement2625([
        52811034, 25909283, 16144682, 17082669, 27570973, 30858332, 40966398, 8378388, 20764389,
        8758491,
    ]),
    Y: FieldElement2625([
        40265304, 26843545, 13421772, 20132659, 26843545, 6710886, 53687091, 13421772, 40265318,
        26843545,
    ]),
    Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    T: FieldElement2625([
        28827043, 27438313, 39759291, 244362, 8635006, 11264893, 19351346, 13413597, 16611511,
        27139452,
    ]),
};

/// The 8-torsion subgroup \\(\mathcal E [8]\\).
///
/// In the case of Curve25519, it is cyclic; the \\(i\\)-th element of
/// the array is \\([i]P\\), where \\(P\\) is a point of order \\(8\\)
/// generating \\(\mathcal E[8]\\).
///
/// Thus \\(\mathcal E[4]\\) is the points indexed by `0,2,4,6`, and
/// \\(\mathcal E[2]\\) is the points indexed by `0,4`.
/// The Ed25519 basepoint has y = 4/5.  This is called `_POINT` to
/// distinguish it from `_TABLE`, which should be used for scalar
/// multiplication (it's much faster).
pub const EIGHT_TORSION: [EdwardsPoint; 8] = EIGHT_TORSION_INNER_DOC_HIDDEN;

/// Inner item used to hide limb constants from cargo doc output.
#[doc(hidden)]
pub const EIGHT_TORSION_INNER_DOC_HIDDEN: [EdwardsPoint; 8] = [
    EdwardsPoint {
        X: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Y: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement2625([
            21352778, 5345713, 4660180, 25206575, 24143089, 14568123, 30185756, 21306662, 33579924,
            8345318,
        ]),
        Y: FieldElement2625([
            6952903, 1265500, 60246523, 7057497, 4037696, 5447722, 35427965, 15325401, 19365852,
            31985330,
        ]),
        Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625([
            41846657, 21581751, 11716001, 27684820, 48915701, 16297738, 20670665, 24995334,
            3541542, 28543251,
        ]),
    },
    EdwardsPoint {
        X: FieldElement2625([
            32595773, 7943725, 57730914, 30054016, 54719391, 272472, 25146209, 2005654, 66782178,
            22147949,
        ]),
        Y: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement2625([
            21352778, 5345713, 4660180, 25206575, 24143089, 14568123, 30185756, 21306662, 33579924,
            8345318,
        ]),
        Y: FieldElement2625([
            60155942, 32288931, 6862340, 26496934, 63071167, 28106709, 31680898, 18229030,
            47743011, 1569101,
        ]),
        Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625([
            25262188, 11972680, 55392862, 5869611, 18193162, 17256693, 46438198, 8559097, 63567321,
            5011180,
        ]),
    },
    EdwardsPoint {
        X: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Y: FieldElement2625([
            67108844, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431,
            67108863, 33554431,
        ]),
        Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement2625([
            45756067, 28208718, 62448683, 8347856, 42965774, 18986308, 36923107, 12247769,
            33528939, 25209113,
        ]),
        Y: FieldElement2625([
            60155942, 32288931, 6862340, 26496934, 63071167, 28106709, 31680898, 18229030,
            47743011, 1569101,
        ]),
        Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625([
            41846657, 21581751, 11716001, 27684820, 48915701, 16297738, 20670665, 24995334,
            3541542, 28543251,
        ]),
    },
    EdwardsPoint {
        X: FieldElement2625([
            34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654, 31548777, 326685,
            11406482,
        ]),
        Y: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement2625([
            45756067, 28208718, 62448683, 8347856, 42965774, 18986308, 36923107, 12247769,
            33528939, 25209113,
        ]),
        Y: FieldElement2625([
            6952903, 1265500, 60246523, 7057497, 4037696, 5447722, 35427965, 15325401, 19365852,
            31985330,
        ]),
        Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625([
            25262188, 11972680, 55392862, 5869611, 18193162, 17256693, 46438198, 8559097, 63567321,
            5011180,
        ]),
    },
];

/// Table containing precomputed multiples of the Ed25519 basepoint \\(B = (x, 4/5)\\).
pub const ED25519_BASEPOINT_TABLE: EdwardsBasepointTable = ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN;

/// Inner constant, used to avoid filling the docs with precomputed points.
#[doc(hidden)]
pub const ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN: EdwardsBasepointTable =
    EdwardsBasepointTable([
        LookupTable([
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    93076338, 52752828, 29566454, 37215328, 54414518, 37569218, 94653489, 21800160,
                    61029707, 35602036,
                ]),
                y_minus_x: FieldElement2625([
                    54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692, 5043384,
                    19500929, 18085054,
                ]),
                xy2d: FieldElement2625([
                    58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918, 11864899,
                    42594502, 29115885,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    54292951, 54132516, 45527619, 11784319, 41753206, 30803714, 55390960, 29739860,
                    66750418, 23343128,
                ]),
                y_minus_x: FieldElement2625([
                    45405608, 6903824, 27185491, 6451973, 37531140, 24000426, 51492312, 11189267,
                    40279186, 28235350,
                ]),
                xy2d: FieldElement2625([
                    26966623, 11152617, 32442495, 15396054, 14353839, 20802097, 63980037, 24013313,
                    51636816, 29387734,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    82745136, 23865874, 24204772, 25642034, 67725840, 16869169, 94896463, 52336674,
                    28944398, 32004408,
                ]),
                y_minus_x: FieldElement2625([
                    16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576, 21778470,
                    7689661, 11199574,
                ]),
                xy2d: FieldElement2625([
                    30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774, 10017326,
                    49359771, 23634074,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    50071967, 13921891, 78054670, 27521000, 27105051, 17470053, 105291517,
                    15006021, 70393432, 27277891,
                ]),
                y_minus_x: FieldElement2625([
                    23599295, 25248385, 55915199, 25867015, 13236773, 10506355, 7464579, 9656445,
                    13059162, 10374397,
                ]),
                xy2d: FieldElement2625([
                    7798537, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, 29715387,
                    66467155, 33453106,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    77970208, 11473153, 27284546, 35535607, 37044514, 46132292, 99976748, 48069538,
                    118779423, 44373810,
                ]),
                y_minus_x: FieldElement2625([
                    4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196, 12483687,
                    54440373, 5581305,
                ]),
                xy2d: FieldElement2625([
                    19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349, 13850243,
                    43430843, 17738489,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    51736881, 20691677, 32573249, 4720197, 107781206, 39429941, 115029100,
                    18329611, 124398787, 21468653,
                ]),
                y_minus_x: FieldElement2625([
                    58559652, 109982, 15149363, 2178705, 22900618, 4543417, 3044240, 17864545,
                    1762327, 14866737,
                ]),
                xy2d: FieldElement2625([
                    48909169, 17603008, 56635573, 1707277, 49922944, 3916100, 38872452, 3959420,
                    27914454, 4383652,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    72262591, 43463716, 68832610, 30776557, 97632468, 39071304, 86589715, 38784565,
                    43156424, 18378665,
                ]),
                y_minus_x: FieldElement2625([
                    36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025, 16520125,
                    30598449, 7715701,
                ]),
                xy2d: FieldElement2625([
                    28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204, 1370707,
                    29794553, 32145132,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    14499452, 64379265, 33917749, 62854211, 95603724, 14271266, 97399599, 10876453,
                    33954766, 35936157,
                ]),
                y_minus_x: FieldElement2625([
                    59913433, 30899068, 52378708, 462250, 39384538, 3941371, 60872247, 3696004,
                    34808032, 15351954,
                ]),
                xy2d: FieldElement2625([
                    27431194, 8222322, 16448760, 29646437, 48401861, 11938354, 34147463, 30583916,
                    29551812, 10109425,
                ]),
            },
        ]),
        LookupTable([
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    53451805, 20399000, 102933977, 45331528, 88556249, 40073815, 64730579,
                    31926875, 77201646, 28790260,
                ]),
                y_minus_x: FieldElement2625([
                    27939166, 14210322, 4677035, 16277044, 44144402, 21156292, 34600109, 12005537,
                    49298737, 12803509,
                ]),
                xy2d: FieldElement2625([
                    17228999, 17892808, 65875336, 300139, 65883994, 21839654, 30364212, 24516238,
                    18016356, 4397660,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    56150002, 25864224, 4776340, 18600194, 27850027, 17952220, 40489757, 14544524,
                    49631360, 34537070,
                ]),
                y_minus_x: FieldElement2625([
                    29253598, 15796703, 64244882, 23645547, 10057022, 3163536, 7332899, 29434304,
                    46061167, 9934962,
                ]),
                xy2d: FieldElement2625([
                    5793284, 16271923, 42977250, 23438027, 29188559, 1206517, 52360934, 4559894,
                    36984942, 22656481,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    39464893, 55615857, 83391519, 22517938, 28414020, 52096600, 24191032, 38096129,
                    53770554, 39054999,
                ]),
                y_minus_x: FieldElement2625([
                    12650548, 32057319, 9052870, 11355358, 49428827, 25154267, 49678271, 12264342,
                    10874051, 13524335,
                ]),
                xy2d: FieldElement2625([
                    25556948, 30508442, 714650, 2510400, 23394682, 23139102, 33119037, 5080568,
                    44580805, 5376627,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    108129445, 29543378, 50095164, 30016803, 60382070, 35475328, 44787558,
                    57661420, 71644630, 35123438,
                ]),
                y_minus_x: FieldElement2625([
                    64853442, 14606629, 45416424, 25514613, 28430648, 8775819, 36614302, 3044289,
                    31848280, 12543772,
                ]),
                xy2d: FieldElement2625([
                    45080285, 2943892, 35251351, 6777305, 13784462, 29262229, 39731668, 31491700,
                    7718481, 14474653,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    69494160, 36008644, 44477543, 33601034, 62670928, 51428448, 67765827, 26317766,
                    91425031, 28300864,
                ]),
                y_minus_x: FieldElement2625([
                    13741529, 10911568, 33875447, 24950694, 46931033, 32521134, 33040650, 20129900,
                    46379407, 8321685,
                ]),
                xy2d: FieldElement2625([
                    21060490, 31341688, 15712756, 29218333, 1639039, 10656336, 23845965, 21679594,
                    57124405, 608371,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    53436113, 18466845, 56219170, 25997372, 61071954, 11305546, 68232832, 60328286,
                    94338261, 33578318,
                ]),
                y_minus_x: FieldElement2625([
                    43864724, 33260226, 55364135, 14712570, 37643165, 31524814, 12797023, 27114124,
                    65475458, 16678953,
                ]),
                xy2d: FieldElement2625([
                    37608244, 4770661, 51054477, 14001337, 7830047, 9564805, 65600720, 28759386,
                    49939598, 4904952,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    91168402, 48171434, 86146020, 18514523, 86874956, 18648002, 72278074, 16191879,
                    69237100, 29227598,
                ]),
                y_minus_x: FieldElement2625([
                    50127693, 4124965, 58568254, 22900634, 30336521, 19449185, 37302527, 916032,
                    60226322, 30567899,
                ]),
                xy2d: FieldElement2625([
                    44477957, 12419371, 59974635, 26081060, 50629959, 16739174, 285431, 2763829,
                    15736322, 4143876,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    69488197, 11839344, 62998462, 27565766, 78383161, 34349388, 67321664, 18959768,
                    23527083, 17096164,
                ]),
                y_minus_x: FieldElement2625([
                    33431108, 22423954, 49269897, 17927531, 8909498, 8376530, 34483524, 4087880,
                    51919953, 19138217,
                ]),
                xy2d: FieldElement2625([
                    1767664, 7197987, 53903638, 31531796, 54017513, 448825, 5799055, 4357868,
                    62334673, 17231393,
                ]),
            },
        ]),
        LookupTable([
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    6721947, 47388255, 43585475, 32003117, 93463156, 21691110, 90474010, 29604699,
                    74499753, 36314231,
                ]),
                y_minus_x: FieldElement2625([
                    4409022, 2052381, 23373853, 10530217, 7676779, 20668478, 21302352, 29290375,
                    1244379, 20634787,
                ]),
                xy2d: FieldElement2625([
                    62687625, 7169618, 4982368, 30596842, 30256824, 30776892, 14086412, 9208236,
                    15886429, 16489664,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    69104920, 43930080, 81455230, 46865633, 60234728, 17116020, 120524529,
                    33952799, 36502408, 32841498,
                ]),
                y_minus_x: FieldElement2625([
                    41801399, 9795879, 64331450, 14878808, 33577029, 14780362, 13348553, 12076947,
                    36272402, 5113181,
                ]),
                xy2d: FieldElement2625([
                    49338080, 11797795, 31950843, 13929123, 41220562, 12288343, 36767763, 26218045,
                    13847710, 5387222,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    48526682, 30138214, 84933706, 64767897, 89853205, 56666252, 75871923, 37172217,
                    47508201, 43925422,
                ]),
                y_minus_x: FieldElement2625([
                    20246567, 19185054, 22358228, 33010720, 18507282, 23140436, 14554436, 24808340,
                    32232923, 16763880,
                ]),
                xy2d: FieldElement2625([
                    9648486, 10094563, 26416693, 14745928, 36734546, 27081810, 11094160, 15689506,
                    3140038, 17044340,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    50948773, 39027126, 31895587, 38299426, 75932378, 43920116, 39884063, 43003044,
                    38334409, 33920726,
                ]),
                y_minus_x: FieldElement2625([
                    19153450, 11523972, 56012374, 27051289, 42461232, 5420646, 28344573, 8041113,
                    719605, 11671788,
                ]),
                xy2d: FieldElement2625([
                    8678006, 2694440, 60300850, 2517371, 4964326, 11152271, 51675948, 18287915,
                    27000812, 23358879,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    119059805, 40688742, 75748150, 30739554, 59873175, 43976173, 67672928,
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            },
        ]),
        LookupTable([
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    76769853, 34259874, 79088928, 28184277, 65480320, 14661172, 60762722, 36179446,
                    95539899, 50337029,
                ]),
                y_minus_x: FieldElement2625([
                    43269631, 25243016, 41163352, 7480957, 49427195, 25200248, 44562891, 14150564,
                    15970762, 4099461,
                ]),
                xy2d: FieldElement2625([
                    29262576, 16756590, 26350592, 24760869, 8529670, 22346382, 13617292, 23617289,
                    11465738, 8317062,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    41615764, 26591503, 99609063, 24135380, 44070139, 31252209, 82007500, 37402886,
                    88078197, 28396915,
                ]),
                y_minus_x: FieldElement2625([
                    46724414, 19206718, 48772458, 13884721, 34069410, 2842113, 45498038, 29904543,
                    11177094, 14989547,
                ]),
                xy2d: FieldElement2625([
                    42612143, 21838415, 16959895, 2278463, 12066309, 10137771, 13515641, 2581286,
                    38621356, 9930239,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    49357223, 31456605, 83653163, 54099563, 118302919, 18605349, 18345766,
                    53705111, 83400343, 28240393,
                ]),
                y_minus_x: FieldElement2625([
                    33879670, 2553287, 32678213, 9875984, 8534129, 6889387, 57432090, 6957616,
                    4368891, 9788741,
                ]),
                xy2d: FieldElement2625([
                    16660737, 7281060, 56278106, 12911819, 20108584, 25452756, 45386327, 24941283,
                    16250551, 22443329,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    47343357, 35944957, 117666696, 14161978, 69014150, 39969338, 71798447,
                    10604806, 104027325, 4782745,
                ]),
                y_minus_x: FieldElement2625([
                    65754325, 14736940, 59741422, 20261545, 7710541, 19398842, 57127292, 4383044,
                    22546403, 437323,
                ]),
                xy2d: FieldElement2625([
                    31665558, 21373968, 50922033, 1491338, 48740239, 3294681, 27343084, 2786261,
                    36475274, 19457415,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    52641566, 32870716, 33734756, 41002983, 19294359, 14334329, 47418233, 35909750,
                    47824192, 27440058,
                ]),
                y_minus_x: FieldElement2625([
                    15121312, 17758270, 6377019, 27523071, 56310752, 20596586, 18952176, 15496498,
                    37728731, 11754227,
                ]),
                xy2d: FieldElement2625([
                    64471568, 20071356, 8488726, 19250536, 12728760, 31931939, 7141595, 11724556,
                    22761615, 23420291,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    16918416, 11729663, 49025285, 36577418, 103201995, 53769203, 38367677,
                    21327038, 32851221, 11717399,
                ]),
                y_minus_x: FieldElement2625([
                    11166615, 7338049, 60386341, 4531519, 37640192, 26252376, 31474878, 3483633,
                    65915689, 29523600,
                ]),
                xy2d: FieldElement2625([
                    66923210, 9921304, 31456609, 20017994, 55095045, 13348922, 33142652, 6546660,
                    47123585, 29606055,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    101757113, 44821142, 55911756, 25655328, 31703693, 37410335, 58571732,
                    20721383, 36336829, 18068118,
                ]),
                y_minus_x: FieldElement2625([
                    49102387, 12709067, 3991746, 27075244, 45617340, 23004006, 35973516, 17504552,
                    10928916, 3011958,
                ]),
                xy2d: FieldElement2625([
                    60151107, 17960094, 31696058, 334240, 29576716, 14796075, 36277808, 20749251,
                    18008030, 10258577,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement2625([
                    44660220, 49210000, 74127342, 29144428, 36794597, 32352840, 65255398, 34921551,
                    92236737, 6671742,
                ]),
                y_minus_x: FieldElement2625([
                    29701166, 19180498, 56230743, 9279287, 67091296, 13127209, 21382910, 11042292,
                    25838796, 4642684,
                ]),
                xy2d: FieldElement2625([
                    46678630, 14955536, 42982517, 8124618, 61739576, 27563961, 30468146, 19653792,
                    18423288, 4177476,
                ]),
            },
        ]),
    ]);

/// Odd multiples of the basepoint `[B, 3B, 5B, 7B, 9B, 11B, 13B, 15B, ..., 127B]`.
pub(crate) const AFFINE_ODD_MULTIPLES_OF_BASEPOINT: NafLookupTable8<AffineNielsPoint> =
    NafLookupTable8([
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                93076338, 52752828, 29566454, 37215328, 54414518, 37569218, 94653489, 21800160,
                61029707, 35602036,
            ]),
            y_minus_x: FieldElement2625([
                54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692, 5043384,
                19500929, 18085054,
            ]),
            xy2d: FieldElement2625([
                58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918, 11864899,
                42594502, 29115885,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                82745136, 23865874, 24204772, 25642034, 67725840, 16869169, 94896463, 52336674,
                28944398, 32004408,
            ]),
            y_minus_x: FieldElement2625([
                16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576, 21778470,
                7689661, 11199574,
            ]),
            xy2d: FieldElement2625([
                30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774, 10017326,
                49359771, 23634074,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                77970208, 11473153, 27284546, 35535607, 37044514, 46132292, 99976748, 48069538,
                118779423, 44373810,
            ]),
            y_minus_x: FieldElement2625([
                4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196, 12483687,
                54440373, 5581305,
            ]),
            xy2d: FieldElement2625([
                19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349, 13850243,
                43430843, 17738489,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                72262591, 43463716, 68832610, 30776557, 97632468, 39071304, 86589715, 38784565,
                43156424, 18378665,
            ]),
            y_minus_x: FieldElement2625([
                36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025, 16520125,
                30598449, 7715701,
            ]),
            xy2d: FieldElement2625([
                28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204, 1370707,
                29794553, 32145132,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                44589852, 26862249, 14201701, 24808930, 43598457, 42399157, 85583074, 32192981,
                54046167, 47376308,
            ]),
            y_minus_x: FieldElement2625([
                60653668, 25714560, 3374701, 28813570, 40010246, 22982724, 31655027, 26342105,
                18853321, 19333481,
            ]),
            xy2d: FieldElement2625([
                4566811, 20590564, 38133974, 21313742, 59506191, 30723862, 58594505, 23123294,
                2207752, 30344648,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                41954014, 62923042, 96790006, 41423232, 60254202, 24130566, 121780363, 32891430,
                103106264, 17421994,
            ]),
            y_minus_x: FieldElement2625([
                25576264, 30851218, 7349803, 21739588, 16472781, 9300885, 3844789, 15725684,
                171356, 6466918,
            ]),
            xy2d: FieldElement2625([
                23103977, 13316479, 9739013, 17404951, 817874, 18515490, 8965338, 19466374,
                36393951, 16193876,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                100695917, 36735143, 64714733, 47558118, 50205389, 17283591, 84347261, 38283886,
                49034350, 9256799,
            ]),
            y_minus_x: FieldElement2625([
                41926547, 29380300, 32336397, 5036987, 45872047, 11360616, 22616405, 9761698,
                47281666, 630304,
            ]),
            xy2d: FieldElement2625([
                53388152, 2639452, 42871404, 26147950, 9494426, 27780403, 60554312, 17593437,
                64659607, 19263131,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                63957664, 28508356, 76391577, 40420576, 102310665, 32691407, 48168288, 15033783,
                92213982, 25659555,
            ]),
            y_minus_x: FieldElement2625([
                42782475, 15950225, 35307649, 18961608, 55446126, 28463506, 1573891, 30928545,
                2198789, 17749813,
            ]),
            xy2d: FieldElement2625([
                64009494, 10324966, 64867251, 7453182, 61661885, 30818928, 53296841, 17317989,
                34647629, 21263748,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                17735022, 27114469, 76149336, 40765111, 43325570, 26153544, 26948151, 45905235,
                38656900, 62179684,
            ]),
            y_minus_x: FieldElement2625([
                2154119, 14782993, 28737794, 11906199, 36205504, 26488101, 19338132, 16910143,
                50209922, 29794297,
            ]),
            xy2d: FieldElement2625([
                29935700, 6336041, 20999566, 30405369, 13628497, 24612108, 61639745, 22359641,
                56973806, 18684690,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                29792811, 31379227, 113441390, 20675662, 58452680, 54138549, 42892249, 32958636,
                31674345, 24275271,
            ]),
            y_minus_x: FieldElement2625([
                7606599, 22131225, 17376912, 15235046, 32822971, 7512882, 30227203, 14344178,
                9952094, 8804749,
            ]),
            xy2d: FieldElement2625([
                32575079, 3961822, 36404898, 17773250, 67073898, 1319543, 30641032, 7823672,
                63309858, 18878784,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                77823924, 52933642, 26572931, 18690221, 109143683, 23989794, 79129572, 53326100,
                38888709, 55889506,
            ]),
            y_minus_x: FieldElement2625([
                37146997, 554126, 63326061, 20925660, 49205290, 8620615, 53375504, 25938867,
                8752612, 31225894,
            ]),
            xy2d: FieldElement2625([
                4529887, 12416158, 60388162, 30157900, 15427957, 27628808, 61150927, 12724463,
                23658330, 23690055,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                102043267, 54823614, 45810225, 19657305, 54297192, 7413280, 66851983, 39718512,
                25005048, 18002658,
            ]),
            y_minus_x: FieldElement2625([
                5403481, 24654166, 61855580, 13522652, 14989680, 1879017, 43913069, 25724172,
                20315901, 421248,
            ]),
            xy2d: FieldElement2625([
                34818947, 1705239, 25347020, 7938434, 51632025, 1720023, 54809726, 32655885,
                64907986, 5517607,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                88543525, 16557377, 80359887, 30047148, 91602876, 27723948, 62710290, 52707861,
                7715736, 61648232,
            ]),
            y_minus_x: FieldElement2625([
                14461032, 6393639, 22681353, 14533514, 52493587, 3544717, 57780998, 24657863,
                59891807, 31628125,
            ]),
            xy2d: FieldElement2625([
                60864886, 31199953, 18524951, 11247802, 43517645, 21165456, 26204394, 27268421,
                63221077, 29979135,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                97491378, 10077555, 94805128, 42472719, 30231379, 17961119, 76201413, 41182329,
                41405214, 31798052,
            ]),
            y_minus_x: FieldElement2625([
                13670592, 720327, 7131696, 19360499, 66651570, 16947532, 3061924, 22871019,
                39814495, 20141336,
            ]),
            xy2d: FieldElement2625([
                44847187, 28379568, 38472030, 23697331, 49441718, 3215393, 1669253, 30451034,
                62323912, 29368533,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                74923758, 35244493, 27222384, 30715870, 48444195, 28125622, 116052444, 32330148,
                92609232, 35372537,
            ]),
            y_minus_x: FieldElement2625([
                39340596, 15199968, 52787715, 18781603, 18787729, 5464578, 11652644, 8722118,
                57056621, 5153960,
            ]),
            xy2d: FieldElement2625([
                5733861, 14534448, 59480402, 15892910, 30737296, 188529, 491756, 17646733,
                33071791, 15771063,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                85239571, 21331573, 119690709, 30172286, 44350959, 55826224, 68258766, 16209406,
                20222151, 32139086,
            ]),
            y_minus_x: FieldElement2625([
                52372801, 13847470, 52690845, 3802477, 48387139, 10595589, 13745896, 3112846,
                50361463, 2761905,
            ]),
            xy2d: FieldElement2625([
                45982696, 12273933, 15897066, 704320, 31367969, 3120352, 11710867, 16405685,
                19410991, 10591627,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                82008850, 34439758, 89319886, 49124188, 34309215, 29866047, 80308709, 27738519,
                71739865, 46909287,
            ]),
            y_minus_x: FieldElement2625([
                36631997, 23300851, 59535242, 27474493, 59924914, 29067704, 17551261, 13583017,
                37580567, 31071178,
            ]),
            xy2d: FieldElement2625([
                22641770, 21277083, 10843473, 1582748, 37504588, 634914, 15612385, 18139122,
                59415250, 22563863,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                76721854, 52814714, 41722368, 35285867, 53022548, 38255176, 93163883, 27627617,
                87963092, 33729456,
            ]),
            y_minus_x: FieldElement2625([
                61915349, 11733561, 59403492, 31381562, 29521830, 16845409, 54973419, 26057054,
                49464700, 796779,
            ]),
            xy2d: FieldElement2625([
                3855018, 8248512, 12652406, 88331, 2948262, 971326, 15614761, 9441028, 29507685,
                8583792,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                76968870, 14808584, 76708906, 57649718, 23400175, 24077237, 63783137, 37471119,
                56750251, 30681804,
            ]),
            y_minus_x: FieldElement2625([
                33709664, 3740344, 52888604, 25059045, 46197996, 22678812, 45207164, 6431243,
                21300862, 27646257,
            ]),
            xy2d: FieldElement2625([
                49811511, 9216232, 25043921, 18738174, 29145960, 3024227, 65580502, 530149,
                66809973, 22275500,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                23499366, 24936714, 38355445, 35908587, 82540167, 39280880, 46809413, 41143783,
                72530804, 49676198,
            ]),
            y_minus_x: FieldElement2625([
                45162189, 23851397, 9380591, 15192763, 36034862, 15525765, 5277811, 25040629,
                33286237, 31693326,
            ]),
            xy2d: FieldElement2625([
                62424427, 13336013, 49368582, 1581264, 30884213, 15048226, 66823504, 4736577,
                53805192, 29608355,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                25190215, 26304748, 58928336, 42665707, 64280342, 38580230, 61299598, 20659504,
                30387592, 32519377,
            ]),
            y_minus_x: FieldElement2625([
                14480213, 17057820, 2286692, 32980967, 14693157, 22197912, 49247898, 9909859,
                236428, 16857435,
            ]),
            xy2d: FieldElement2625([
                7877514, 29872867, 45886243, 25902853, 41998762, 6241604, 35694938, 15657879,
                56797932, 8609105,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                54245189, 32562161, 57887697, 19509733, 45323534, 37472546, 27606727, 59528498,
                74398957, 44973176,
            ]),
            y_minus_x: FieldElement2625([
                28964163, 20950093, 44929966, 26145892, 34786807, 18058153, 18187179, 27016486,
                42438836, 14869174,
            ]),
            xy2d: FieldElement2625([
                55703901, 1222455, 64329400, 24533246, 11330890, 9135834, 3589529, 19555234,
                53275553, 1207212,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                33323313, 35603165, 79328585, 6017848, 71286345, 23804207, 86644124, 44008367,
                55775078, 31816581,
            ]),
            y_minus_x: FieldElement2625([
                64814718, 27217688, 29891310, 4504619, 8548709, 21986323, 62140656, 12555980,
                34377058, 21436823,
            ]),
            xy2d: FieldElement2625([
                49069441, 9880212, 33350825, 24576421, 24446077, 15616561, 19302117, 9370836,
                55172180, 28526191,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                95404934, 26757208, 123864063, 4572839, 69249194, 43584425, 53559055, 41742046,
                41167331, 24643278,
            ]),
            y_minus_x: FieldElement2625([
                35101859, 30958612, 66105296, 3168612, 22836264, 10055966, 22893634, 13045780,
                28576558, 30704591,
            ]),
            xy2d: FieldElement2625([
                59987873, 21166324, 43296694, 15387892, 39447987, 19996270, 5059183, 19972934,
                30207804, 29631666,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                67444156, 16132892, 88330413, 37924284, 68147855, 57949418, 91481571, 24889160,
                62329722, 50712214,
            ]),
            y_minus_x: FieldElement2625([
                56922508, 1347520, 23300731, 27393371, 42651667, 8512932, 27610931, 24436993,
                3998295, 3835244,
            ]),
            xy2d: FieldElement2625([
                16327050, 22776956, 14746360, 22599650, 23700920, 11727222, 25900154, 21823218,
                34907363, 25105813,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                59807886, 12089757, 115624210, 41476837, 67589715, 26361580, 71355762, 44268661,
                67753061, 13128476,
            ]),
            y_minus_x: FieldElement2625([
                7174885, 26592113, 59892333, 6465478, 4145835, 17673606, 38764952, 22293290,
                1360980, 25805937,
            ]),
            xy2d: FieldElement2625([
                40179568, 6331649, 42386021, 20205884, 15635073, 6103612, 56391180, 6789942,
                7597240, 24095312,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                54776568, 36935932, 18757261, 41429535, 67215081, 34700142, 86560976, 61204154,
                26496794, 19612129,
            ]),
            y_minus_x: FieldElement2625([
                46701540, 24101444, 49515651, 25946994, 45338156, 9941093, 55509371, 31298943,
                1347425, 15381335,
            ]),
            xy2d: FieldElement2625([
                53576449, 26135856, 17092785, 3684747, 57829121, 27109516, 2987881, 10987137,
                52269096, 15465522,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                80033010, 26264316, 72380996, 10039544, 94605936, 30615493, 60406855, 30400829,
                120765849, 45301372,
            ]),
            y_minus_x: FieldElement2625([
                35668062, 24246990, 47788280, 25128298, 37456967, 19518969, 43459670, 10724644,
                7294162, 4471290,
            ]),
            xy2d: FieldElement2625([
                33813988, 3549109, 101112, 21464449, 4858392, 3029943, 59999440, 21424738,
                34313875, 1512799,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                29494960, 28240930, 51093230, 28823678, 92791151, 54796794, 77571888, 37795542,
                75765856, 10649531,
            ]),
            y_minus_x: FieldElement2625([
                63536751, 7572551, 62249759, 25202639, 32046232, 32318941, 29315141, 15424555,
                24706712, 28857648,
            ]),
            xy2d: FieldElement2625([
                47618751, 5819839, 19528172, 20715950, 40655763, 20611047, 4960954, 6496879,
                2790858, 28045273,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625([
                85174457, 55843901, 111946683, 31021158, 32797785, 48944265, 78338887, 31144772,
                82688001, 38470222,
            ]),
            y_minus_x: FieldElement2625([
                49664705, 3638040, 57888693, 19234931, 40104182, 28143840, 28667142, 18386877,
                18584835, 3592929,
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